Preparation

In a resealable jar, place the vanilla bean, seeds, and 1/2 cup of the oil. Shake to combine, and let sit at room temperature overnight or up to a week.

If using fresh corn, shuck the kernels off 11 of the cobs into a large bowl, setting aside 1 cob (or 1/2 cup frozen kernels) for garnish.

Position a rack in the center of the oven; heat the broiler on high.

Melt the butter in a large Dutch oven or other heavy-duty pot over medium heat. Add the leeks, onion, and garlic. cook, stirring occasionally, until the mixture softens and turns translucent, about 5 minutes. Add the corn kernels and cook, stirring occasionally, until they begin to soften, about 6 minutes. Add the broth, reduce the heat to low, and cover with the lid ajar. Simmer for 45 minutes, stirring occasionally. Remove from the heat, season to taste with salt and pepper, and stir to combine. Let cool slightly.

In the meantime, brush the remaining ear of corn with the 1 tsp. oil, and transfer to a large foil-lined rimmed baking sheet. Broil, turning the cob every 5 minutes, until charred on all sides, 10 to 12 minutes. When cool, cut the corn from the cob. Alternatively, cook the reserved frozen kernels in a small skillet over medium-high heat, stirring, until lightly charred. Set aside.

Transfer the corn and leek mixture to a blender in batches, and purée until smooth, about 1 minute per batch. Strain each batch through a fine-mesh strainer set over a large bowl, pushing the mixture through with a silicone spatula. Discard the solids in the strainer between batches. Cover with plastic wrap, and refrigerate until chilled, 4 hours or up to overnight.

To serve, let the soup sit at room temperature for 15 minutes. Whisk in the cream, and season to taste with salt and pepper. Transfer to serving bowls, and garnish with the charred corn kernels and a drizzle of the vanilla oil. Top with flaky sea salt, and serve with a lime wedge.